Conventionally, there has been widely known an air-fuel ratio control apparatus which includes a three-way catalyst disposed in an exhaust passage of an internal combustion engine, and an upstream air-fuel-ratio sensor and a downstream air-fuel-ratio sensor disposed in the exhaust passage so as to be located upstream and downstream, respectively, of the three-way catalyst. This air-fuel ratio control apparatus calculates an air-fuel ratio feedback quantity on the basis of the outputs of the upstream and downstream air-fuel-ratio sensors such that the air-fuel ratio of the air-fuel mixture supplied to the engine (air-fuel ratio of the engine) coincides with the stoichiometric air-fuel ratio, and feedback-controls the air-fuel ratio of the engine on the basis of the air-fuel ratio feedback quantity. Furthermore, there has been also widely known an air-fuel ratio control apparatus which calculates an air-fuel ratio feedback quantity on the basis of the output of the upstream air-fuel-ratio sensor only, and feedback-controls the air-fuel ratio of the engine on the basis of the air-fuel ratio feedback quantity. The air-fuel ratio feedback quantity used in each of those air-fuel ratio control apparatuses is a control quantity commonly used for all of the cylinders.
Incidentally, in general, an electronic-fuel-injection-type internal combustion engine has at least one fuel injection valve (fuel injector) at each of the cylinders or at each of intake ports communicating with the respective cylinders. Accordingly, when the characteristic/property of the fuel injection valve of a certain cylinder changes to inject fuel in a quantity excessively larger than an instructed fuel injection quantity, only the air-fuel ratio of an air-fuel mixture supplied to that certain cylinder (the air-fuel ratio of the certain cylinder) greatly changes toward the rich side. That is, the degree of air-fuel ratio non-uniformity among the cylinders (inter-cylinder air-fuel ratio variation; inter-cylinder air-fuel ratio imbalance) increases. In other words, there arises an imbalance among “cylinder-by-cylinder air-fuel ratios (the air-fuel ratios of the cylinders)”, each of which is the air-fuel ratio of the air-fuel mixture supplied to each of the cylinders.
In such a case, the average of the air-fuel ratios of the air-fuel mixtures supplied to the entire engine becomes an air-fuel ratio in the rich side in relation to (with respect to) the stoichiometric air-fuel ratio. Accordingly, by the air-fuel ratio feedback quantity commonly used for all of the cylinders, the air-fuel ratio of the above-mentioned certain cylinder is changed toward the lean side so as to approach the stoichiometric air-fuel ratio, and, at the same time, the air-fuel ratios of the remaining cylinders are changed toward the lean side so as to deviate from the stoichiometric air-fuel ratio. As a result, the average of the air-fuel ratios of the air-fuel mixtures supplied to the entire engine becomes substantially equal to the stoichiometric air-fuel ratio.
However, since the air-fuel ratio of the certain cylinder is still in the rich side in relation to the stoichiometric air-fuel ratio and the air-fuel ratios of the remaining cylinders are in the lean side in relation to the stoichiometric air-fuel ratio, combustion of the air-fuel mixture in each of the cylinders fail to become complete combustion. As a result, the amount of emissions (the amount of unburned combustibles and the amount of nitrogen oxides) discharged from each of the cylinders increases. Therefore, even when the average of the air-fuel ratios of the air-fuel mixtures supplied to the cylinders of the engine is equal to the stoichiometric air-fuel ratio, the increased emissions cannot be completely removed by the three-way catalyst. Consequently, the amount of emissions may increase.
Accordingly, in order to prevent emissions from increasing, it is important to detect a state in which the degree of air-fuel ratio non-uniformity among the cylinders becomes excessively large (generation of an inter-cylinder air-fuel-ratio imbalance state) and take some measures against the imbalance state. It should be noted that, inter-cylinder air-fuel-ratio imbalance also occurs, for example, in the case where the characteristic of the fuel injection valve of the certain cylinder changes to inject fuel in a quantity excessively smaller than the instructed fuel injection quantity.
One of such conventional apparatuses for determining whether or not an inter-cylinder air-fuel-ratio imbalance state has occurred is configured so as to obtain a trace/trajectory length of an output value (output signal) of an air-fuel-ratio sensor (the above-mentioned upstream air-fuel-ratio sensor) disposed at an exhaust merging/aggregated region into which exhaust gases from a plurality of cylinders of an engine merge, compare the trace length with a “reference value which changes in accordance with the rotational speed of the engine,” and determine whether or not an inter-cylinder air-fuel-ratio imbalance state has occurred on the basis of the result of the comparison (see, for example, U.S. Pat. No. 7,152,594).
It should be noted that, in the present specification, the expression “inter-cylinder air-fuel-ratio imbalance state (excessive inter-cylinder air-fuel-ratio imbalance state)” means a state in which the difference between the cylinder-by-cylinder air-fuel ratios is equal to or greater than an allowable value; in other words, it means an inter-cylinder air-fuel-ratio imbalance state in which the amount of unburned combustibles and/or nitrogen oxides exceeds a prescribed value. The determination as to whether or not an “inter-cylinder air-fuel-ratio imbalance state” has occurred will be simply referred to as “inter-cylinder air-fuel-ratio imbalance determination” or “imbalance determination.” Moreover, a cylinder supplied with an air-fuel mixture whose air-fuel ratio deviates from the air-fuel ratio of air-fuel mixtures supplied to the remaining cylinders (for example, an air-fuel ratio approximately equal to the stoichiometric air-fuel ratio) will also be referred to as an “imbalanced cylinder.” The air-fuel ratio of the air-fuel mixture supplied to such an imbalanced cylinder will also be referred to as the air-fuel ratio of the imbalanced cylinder.” The remaining cylinders (cylinders other than the imbalanced cylinder) will also be referred to as “normal cylinders” or “balanced cylinders.” The air-fuel ratio of air-fuel mixtures supplied to such normal cylinders will also be referred as the “air-fuel ratio of the normal cylinders” or the “air-fuel ratio of the balanced cylinders.”
In addition, a parameter (e.g., the trace length of the output value of the above-mentioned air-fuel-ratio sensor), whose absolute value increases (monotonously) as the difference between the cylinder-by-cylinder air-fuel ratios (the difference between the air-fuel ratio of the imbalanced cylinder and those of the normal cylinders) becomes large, and which is compared with a threshold value for imbalance determination when imbalance determination is performed will also be referred to as an “imbalance determination parameter.” This imbalance determination parameter is obtained on the basis of the output value of an air-fuel-ratio sensor.